A Probe Into The Concept Of "Series Limit" Myth In High School Students And Its Transformation

Calculus is the landmark invention in the history of mathematics. As a powerful tool, calculus is irreplaceable not only to modern engineering technology, but also to information technology and scientific research. The limit of a number sequence is the basic concepts of calculus. It links up the finite and the infinite, the constants and variables. It makes up the deficiency in the theoretical basis of calculus. However, due to the abstraction of the concept, it makes students have difficulties in learning and result to some misunderstanding in the concept of the limit of a number sequence for many students. Ideas that are not the same as scientists are called misconceptions. Misconceptions are extentive and obstinate. They would hinder students’comprehension of the right conception. Therefore, students’misconeeptions should be fully understanded in mathematical teaching, and design teaehing strategies to promote transformation of misconception.It become the key to improve mathematical teaching strategies. Therefore, teachers need to adopt some of the methods and means probing misconceptions students may exist. Two-Tier Diagnostic Assessment as one of the current mainstream misconceptions diagnostic method has been widely used in domestic and foreign study in some subject such as physics and chemistry, but it is rarely used in mathmatics. This study attempts to use Two-Tier Diagnostic Assessment for e develope diagnostic tool TDLSM, which is used to explore students’misconceptions after learning limit chapters in school. After analyze the causes of these misconceptions, we fulfill following four asepects:First, based on collecting and sorting out related literature about misconceptions and conceptual change, authour discuss the characteristics, causes and methods of misconceptions, expound the basic theory of conceptual change, and clarify the research foundation.Second, based on the literature study and referring to two-stage diagnostic tool developing process Treagust (1988) proposed,author develop the tool called TDLSM to diagnostic students’misconceptions. Third, adopting TDLSM to diagnostic high school students’misconceptions in the conception of the limit of a number sequence, and analyzes the results of the survey. Respondents are grade11studengts from Shanghai two district-level key high schools and have been studying the sequence limit chapters.Fourth, based on analysis of the survey results, discuss the reasons for the different schools limit the number of columns on the conceptual understanding of the situation and misconceptions limit the number of columns formed, and accordingly proposed changes limit the number of columns misconceptions teaching strategies.The results show that the number of high school students in a descriptive definition of the limits of the column, the column tends to limit the number of ways to understand the concept of infinity, infinite geometric series and the concept of algorithms limit the number of columns, etc. There are misconceptions; these misconceptions of students learning from past life experiences, inappropriate analogy, the lack of a broader concept, lack of background knowledge epistemological barriers and other disciplines.According to the research and current teaching practice, the authour think that reasonably applying some teaching strategies such as mathematical history-cognitive analysis, concept map, comparative, cooperative teaching and object teaching and so on into teaching the limit of a number sequence conception will effectively promote students to change misconceptions of photosynthesis, the improve the quality of the limit of a number sequence concetpion teaching.